The last of the Tampa Bay Buccaneers' eight drives was the only one that did not cross into Kansas City territory on Sunday afternoon at raucous Arrowhead Stadium. But it got just far enough.

The Buccaneers defeated the Kansas City Chiefs, 19-17, on Sunday, behind an offense that converted 11 of 15 third down tries, ran up 442 net yards and turned the ball over just once against the NFL's best takeaway defense. The Chiefs pulled within two points with a touchdown in the game's final three minutes but Jameis Winston and Mike Evans combined for one final first down to allow the offense to drain all but 23 seconds off the clock.

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That drive ended at the Bucs' 49 yard line. Each of the Bucs' first seven drives got as far as the Chiefs' 36 and included at least three first downs. Winston's final pass to Evans converted a third-and-three and completed a 331-yard passing day for the second-year passer.

"The huddle was just, 'It's about want-to,'" said Winston, describing the game's final third-down situation. "At the end, I asked the guys, 'Who wants it?' And they said, 'We want it!' So I said, 'Okay, let's go get it.'

"We played as a family. When you play as a family, it gets us excited out there. Everyone had each other's backs and that was a great win."

The win improved the Buccaneers to 5-5, pulling them within a game of the idle Atlanta Falcons (6-4) in the NFC South. The Carolina Panthers and New Orleans Saints are both 4-6 after the Panthers beat the Saints on Thursday night.

"We have to keep building," said Winston. "It's one day at a time, one win at a time. We have to keep building. Obviously, we're on the up-and-up but we've got to keep producing."

The Buccaneers won for the fourth time in five road trips this season, and did so in perhaps their most impressive fashion yet. Playing in what has been measured as the loudest outdoor stadium in the country, the Chiefs had won 10 straight home games, dating back to 2015.

"I think we just come together as a family," said safety Chris Conte of the Bucs' road prowess. "We have a really close locker room, so we have to pull together and be tough. When we travel we do everything we can and we come together as a team and get it done."

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Conte turned in the biggest defensive play of the game for the second weekend in a row. After scoring his first career touchdown on a pick-six to start the Bucs' 36-10 rout of Chicago last Sunday, he intercepted a fourth-quarter Alex Smith pass in the end zone and returned it 55 yards to midfield. The Chiefs were threatening to take a 17-12 lead but Conte's takeaway set up a Buccaneer drive that ended in Jameis Winston's three-yard touchdown pass to rookie TE Alan Cross. It was Cross's first career touchdown, on just his second NFL reception.

"That's his play all the way," said Winston. "Alan Cross has been working his tail off since he first stepped foot in this building. I'm proud of him and I'm proud for his family that he got his first career touchdown."

Winston completed 24 of 39 passes and utilized all of his available weapons. Evans led the way with six catches for 105 yards but Doug Martin, Adam Humphries, Cecil Shorts and Russell Shepard all caught between four and seven passes for between 42 and 62 yards.

"Complementary football, man," said Winston. "Chris Conte has been putting in a lot of work these last three weeks. He's been showing up and showing out. Congrats to him. That defense held strong in their red zone at their home. That was a big stop, so as an offense we had to take it upon ourselves and score for that defense."

The Buccaneers' only turnover was a Winston fumble in the first quarter when the ball slipped from his hand as he was trying to make a quick throw. That was part of a frustrating start for Tampa Bay's offense, as it repeatedly drove into the red zone only to come away with minimal points. Still, the accurate kicking of rookie Roberto Aguayo – four field goals in four attempts plus an extra point for a career-high 13 points – kept the Bucs in a tight game and allowed them to take the lead in the second half.

Tampa Bay also remained balanced on offense, rushing 34 times for 116 yards. Doug Martin, in his second game back from a lengthy injury absence, was sharp but often ran into a crowd, toting the ball 24 times for 63 yards. The Bucs' defense held a good Kansas City rushing attack to 82 yards and only allowed three points on the Chiefs' first two goal-to-go opportunities.

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The Buccaneers moved the ball very well in the first half but had trouble finishing their drives, which led to a one-point deficit at the intermission. Tampa Bay converted six of eight third down tries – all on Winston passes – and did not punt, but turned three red zone incursions into just six points. The Bucs' first scoring opportunity ended in a fumble by Winston and the next two produced short field goals. A sharp two-minute drill allowed the visitors to counter Alex Smith's 11-yard touchdown run with a third field goal, making it 10-9. The Bucs ran at least nine plays and gained at least 52 net yards on all four of their first-half possessions.

The Chiefs' offense chewed up the first half of the opening quarter on a 13-play 74-yard field goal drive. Bucs LB Daryl Smith forced fumble by WR Chris Conley near midfield but it was recovered by Ware. TE Travis Kelce caught a 17-yard pass to get the ball down to the Bucs' 30 before two Ware runs and a Tyreek Hill underneath handoff led to a first-and-goal at the four. Tampa Bay's defense held there, in tanks part to a tricky handoff to the tight end Kelce that DE William Gholston sniffed out and dropped for a loss of five. Cairo Santos nailed a 22-yard field goal for the game's first points.

The Buccaneers countered with a strong drive of their own, with Winston converting three straight third downs on passes to Humphries, Brate and Shepard. However, after a first-down run of five yards by Martin made it second-and-five at the Chiefs' 16, the Bucs' coughed it up when the ball slipped from Winston's hand as he tried to throw a quick screen pass. The result was a fumble that Kansas City recovered at their own 21.

The Bucs' defense minimized the damage after the turnover by forcing a three-and-out on Noah Spence's stop of Ware on a third-and-two run. However, a 58-yard punt by Dustin Colquitt flipped the field, making the Bucs start again at their own 26. One play, a 23-yard completion to Evans down the left seam, put the ball near midfield, and Cecil Shorts tacked on 19 more on a crossing route. Winston converted yet another third down with a hard pass to Brate at the eight but the next third down came up empty when Evans couldn't quite hang on to a lob into the back left of the end zone. The Bucs settled for Aguayo's 31-yard field goal and a 3-3 tie with 10 minutes left in the first half.

The Bucs' defense forced another three-and-out, with CB Alterraun Verner breaking up a third-and-one pass intended for Hill. On the first play of the ensuing drive, Winston faked a handoff and rolled left, then eventually threw all the way back across the field to Martin, who had room to dash for 27 yards to the Chiefs' 39. Three plays later, Winston fired over the middle to Shorts, with the ball originally spotted at the Chiefs' 30, just short of the first-down marker. Dirk Koetter threw the challenge flag to have the spot reviewed and won, with the ball moved just passed the 29. However DL Rakeem Nunez-Roches blew through the line on the next span and trapped Martin for a loss of six yards. Winston made up for it with a perfect lob pass down the left sideline to Evans at the four-yard line. Unfortunately, the drive stalled there and once again Tampa Bay settled for a field goal, this one a 23-yarder.

The Chiefs' offense got untracked by throwing deep, with Hill hauling in a 42-yarder to the Bucs' 38. Ware took a direct snap on third-and-one and burst up the middle for 15 yards to the 14-yard line. Two plays later, the Bucs covered well in the end zone but Smith saw a crease up the middle and ran through it for an 11-yard touchdown to put the Chiefs on top, 10-6.

The Bucs had 1:13 left in the half after the ensuing touchback and used it to narrow the Chiefs' lead to one point. A 19-yard catch by Russell Shepard got the ball to midfield and Winston then converted a third-and-10 with an 18-yard laser over the middle to Humphries. One more short out to Humphries got the ball to the Chiefs' 23 with 11 seconds to play and Koetter, with no timeouts left, sent Aguayo out to try a 41-yard field goal. The rookie made it 3-for-3 in the first half by driving it down the middle.

The Bucs got the ball first to start the second half and once again put together a lengthy drive that wasn't quite long enough to breach the end zone. A 12-yard run and a 14-yard catch on a screen by Martin were the big plays in a march that fizzled at the 18-yard line, leading to Aguayo's 36-yarder and a 12-10 lead for the visitors.

The Chiefs got their next possession across midfield but were forced to punt from the Bucs' 36, and Colquitt bounced it down at the four-yard line. Two straight Martin runs up the middle moved the chains, and then rookie RB Peyton Barber relieved Martin and ran four times for 22 yards to help get the ball across midfield. However, a pair of penalties led to the Bucs' first punt of the day, and a touchback plus a holding penalty on the kicking unit gave the ball back to Kansas City at their 30-yard line.

Kansas City quickly took the game's momentum back, as Smith hit Kelce down the right sideline for a gain of 44 to the Bucs' 10-yard line. However, two plays later Conte cut in front of Albert Conley in the end zone for an interception and returned it 55 yards to the midfield stripe.

Winston found Shepard for a gain of 16 to the Chiefs 29 on third-and-three moments later, then converted the next third down with a strike to Shorts at the Kansas City 11. A Martin run up the gut got nine, but he lost a yard on the subsequent tote. On third-and-three from the four, Winston faked a handoff and threw to a wide-open cross for a touchdown to make it 19-10 with 6:26 to play.

Against a Buccaneers defense that was playing back to avoid big plays and run the clock, Smith drove his team 78 yards on 12 plays, ending in a three-yard touchdown pass to Albert Wilson. However, the drive chewed four minutes off the clock and put the Bucs in position to run it out with a successful four-minute drill.